Abstract

We analyze the geometric structure and properties of a certain class of subsets of Rd\mathbb{R}^d, here called multicones, which are natural generalizations of the classical cones. For them we introduce and investigate a suitable extension of the concept of duality, which allows us to treat in a convenient way many issues related to their invariance and strict invariance for real matrices.

Author information

Contact details are reproduced from the original publication and may be historical.

Michela Brundu

Dip. di Matematica e Geoscienze, Università di Trieste, 34127 Trieste, Italy

brundu@units.it

Marino Zennaro

Dip. di Matematica e Geoscienze, Università di Trieste, 34127 Trieste, Italy

zennaro@units.it

Keywords

  • Cone
  • multicone
  • duality
  • matrix
  • invariant set
  • leading eigenvalue
  • leading eigenvector

Mathematics Subject Classification

15A18, 15A48, 52A30, 52B55

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Suggested citation

M. Brundu, M. Zennaro. “Multicones, Duality and Matrix Invariance.” Journal of Convex Analysis 26 (2019), No. 3, 1021–1052. https://doi.org/10.68381/jca26055

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.